Students in this video, let's discuss perpendicular lines now, let's have two lines and let them one
and aim to be the slopes of these two lines.
All right.
Now, if these two lines are perpendicular, that is if they are intersecting at an angle, forming
90 degree.
Right.
Then M1 and M2 will have this relation that is M1 into M2 will be equal to minus one.
Now, why is that so we know that the angle between two lines is given by Dante is equal to more of
in one minus M2, two by one plus M1, M2 right now, when M1 into M2 is equal to minus one over here
you can see that the denominator becomes zero.
Right.
And division by zero is not defined.
So when M1 into M2 is equal to minus one, Dante De is equal to infinity or it is not defined.
Now, in technology, you will have learned that Danto is infinity when data is equal to 90 degrees.
That's why when two given lines with Slope's M1 and M2 are perpendicular, then M1 into M2 will be equal
to minus one.
All right, let's take two lines where this is true.
Let's have a X plus by plus one is equal to zero and B minus Ebeye.
Let's see, two is equal to zero.
All right.
Now why did I constructed like this?
You can see that I have a B over here and it has been interchanged and over here you have a plus sign
and this has become minus.
Let's try to see why that is so.
All right.
Let me make some space over here.
What is the slope of the first line over here?
You can see that the slope over here, M1 is minus eight by B, right.
Or do you find that you have to write it in the form Y is equal to an explicit.
So you will get that Y is equal to minus eight by B, X plus something right up the slope over here
is minus Abib.
What about the slope over here you will see that the slope over here is equal to be by eight.
And when you multiply these two together you can see that you will get minus one.
Right, minus B into B, it gives you minus one.
Therefore there is this an interesting property.
If you are given one line and if you want to write the line, which is perpendicular to this line,
you just need to change the coefficients and change the sign over here.
That is, let me make some space over here.
If you have given X plus by places equal to zero and you want to write a line that is perpendicular
to this line, that line would have the coefficient that's over here for white for X.
That is because and the coefficient for it will be given to be that is a right.
But all you need to change the sine so this will become minus a white plus int. equals zero.
So this line will be perpendicular to this line.
And we have seen the reason over here.
Over here the slope is minus Ebi B and over here the slope is B by and if you multiply them you get
minus one.
And that makes tanty the equal to infinity and hence the it is equal to 90 degrees.